The present invention relates in general to the art of reshaping the heads of railway track rails and has specific reference to a machine for reshaping rail heads which comprises one or a plurality of grinding units adapted to operate along one running rail, with means for positioning and feeding the cutting tool or tools in relation to the head, the grinding unit or units being disposed around the rail head for the purpose of grinding one or several faces corresponding to theoretical tangents along one and/or a plurality of generatrices of the theoretical cross-section of the rail.